Publications [#371975] of Alexander J Dunlap

Papers Published

1. Dunlap, A; Graham, C; Ryzhik, L, Stationary solutions to the stochastic burgers equation on the line, Communications in Mathematical Physics, vol. 382 no. 2 (March, 2021), pp. 875-949 [doi]
   (last updated on 2026/01/15)

   Abstract:
   We consider invariant measures for the stochastic Burgers equation on $\mathbb{R}$, forced by the derivative of a spacetime-homogeneous Gaussian noise that is white in time and smooth in space. An invariant measure is indecomposable, or extremal, if it cannot be represented as a convex combination of other invariant measures. We show that for each $a\in\mathbb{R}$, there is a unique indecomposable law of a spacetime-stationary solution with mean $a$, in a suitable function space. We also show that solutions starting from spatially-decaying perturbations of mean-$a$ periodic functions converge in law to the extremal space-time stationary solution with mean $a$ as time goes to infinity.